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1. Three-loop effective potential for softly broken supersymmetry

   https://doi.org/10.1103/PhysRevD.109.015019  

   Martin, Stephen P (January 2024, Physical Review D)

   The effective potential has been previously calculated through three-loop order, in Landau gauge, for a general renormalizable theory using dimensional regularization. However, dimensional regularization is not appropriate for softly broken supersymmetric gauge theories, because it explicitly violates supersymmetry. In this paper, I obtain the three-loop effective potential using a supersymmetric regulator based on dimensional reduction. Checks follow from the vanishing of the effective potential in examples with supersymmetric vacua, and from renormalization scale invariance in examples for which supersymmetry is broken, either spontaneously or explicitly by soft terms. As byproducts, I obtain the three-loop Landau gauge anomalous dimension for the scalar component of a chiral supermultiplet, and the beta function for the field-independent vacuum energy. 

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2. Twistors, Hyper-Kaehler Manifolds, and Complex Moduli

   https://doi.org/10.1007/978-3-319-67519-0  

   LeBrun, Claude (November 2017, Springer INdAM series)

   Chiossi, Simon; Fino, Anna; Musso, Emilio; Podesta, Fabio; Vezzoni, Luigi (Ed.)

   A theorem of Kuranishi (Ann Math 75(2):536–577, 1962) tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli space contains a sequence of regions for which the local dimension tends to infinity. These examples naturally arise from the twistor theory of hyper-Kähler manifolds. 

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3. Constructing operator basis in supersymmetry: a Hilbert series approach

   https://doi.org/10.1007/JHEP04(2023)097  

   Delgado, Antonio; Martin, Adam; Wang, Runqing (April 2023, Journal of High Energy Physics)

   A bstract In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of motion and integration by parts. In addition, we derive the maps between the correction spaces. This technique allows us to calculate the number of independent operators involving chiral and antichiral superfields to arbitrarily high mass dimension. Using this method, we give several illustrative examples. 

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4. Differentiable VQ-VAE's for Robust White Matter Streamline Encodings

   Lizarraga, A; Taraku, B; Honig, E; Wu, Y N; Joshi, S H (May 2024, IEEE International Symposium on Biomedical Imaging (ISBI))

   Given the complex geometry of white matter streamlines, Autoencoders have been proposed as a dimension-reduction tool to simplify the analysis streamlines in a low-dimensional latent spaces. However, despite these recent successes, the majority of encoder architectures only perform dimension reduction on single streamlines as opposed to a full bundle of streamlines. This is a severe limitation of the encoder architecture that completely disregards the global geometric structure of streamlines at the expense of individual fibers. Moreover, the latent space may not be well structured which leads to doubt into their interpretability. In this paper we propose a novel Differentiable Vector Quantized Variational Autoencoder, which are engineered to ingest entire bundles of streamlines as single data-point and provides reliable trustworthy encodings that can then be later used to analyze streamlines in the latent space. Comparisons with several state of the art Autoencoders demonstrate superior performance in both encoding and synthesis. 

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5. Moduli spaces and period mappings of genus one fibered K3 surfaces

   Farb, Benson; Looijenga, Eduard (October 2025, Journal of differential geometry)

   In this paper we construct various moduli spaces of K3 sur- faces M equipped with a surjective holomorphic map π : M →P1 with generic fiber a complex torus (e.g., an elliptic fibration). Examples in- clude moduli spaces of such maps with primitive fibers; with reduced, irreducible fibers; equipped with a section. Such spaces are closely re- lated to the moduli space of Ricci-flat metrics on M. We construct period mappings relating these moduli spaces to locally symmetric spaces, and use these to compute their orbifold fundamental groups. 

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